Fractal characterization of speech waveform graphs

doi:10.1016/0097-8493(86)90068-3

Computers & Graphics

Volume 10, Issue 1, 1986, Pages 51-61

https://doi.org/10.1016/0097-8493(86)90068-3 Get rights and content

Abstract

Mandelbrot's fractal geometry has provided a new qualitative and quantitative approach for understanding the complex shapes of nature. In this paper, the fractal structure of speech waveforms is studied at time scales where important phonetic and prosodic information reside. We have found, using methods commonly applied to complex shapes such as coastlines, that speech exhibits fractal characteristics. We have made measurements of the fractal dimension (D) for sentences and have found that D ∼ 1.66 with little change between speakers and sentences.

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Many studies were done to find the upper and lower bounds for the box size. Chen et al. (1993) proposed a theoretical justification for a restriction on the smallest box size inspired by the work of (Pickover and Khorasani, 1986). Also Bisoi and Mishra (2001) established a lower bound of the box size to ensure accurate results.
Public concerns and official pressures around environmental protection as well as exhausting petroleum resources have brought about preferences in studying and applying environmental-friendly polymers instead of synthetic petroleum-based polymers. For this aim, biopolymers can have outstanding advantages in biodegradability by saving time, energy and effort spent on increasingly costs of polymeric wastes. Natural starch (being studied in this work), as one of the most abundant natural resources for polymer materials, is inexpensive and biodegradable. As starch necessarily needs for modifications and processing before being used as ideal green polymer material, it is vital to perform feature extraction and defect detection measures in structure by some method like image analysis. Fractal as a new geometry has circumstantially progressed recently in the fields of image processing, physical space–time, medical image analysis, electrochemical patterns, digital images, sounds etc. Box Count Fractal Dimension as a very important and popular part of fractal geometry can be a useful factor in feature extraction and pattern recognition. This paper presents a new method for defect detection in the structure of natural starch modification images using the fractal dimension (FD) along with mean and standard deviation of image color. This is performed via feature extraction based on artificial intelligence by MatLab R2013a for box counting algorithms. Otsu’s graythresh method by MatLab R2013a is applied to binarize the images. The results of proposed methodology are illustrated as log–log curves where the fractal dimensions are recognized by curve fitting (CF) tool with more than 95% accuracy. The outputs express that starch samples’ FD vary in the range from 1.636 to 1.926 among which the last is identified as non-defective polymer. Non-defective feature is of great importance for quality control measures and chemical reactivity being here highlighted as biodegradability.
Analysing roughness of surface through fractal dimension: A review
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Though it is better than others, this DBC technique also suffers some kind of drawbacks like over-counting (OC) or under-counting (UC) problem reported by Chen et al. [37]. The main limitation of box counting method is to choose appropriate box size, so Chen et al. [9] was reported about the theoretical justification for a constraint on the smallest box size encouraged by the work of Pickover and Khorasani [38]. Later on the basics of boundary selection, Bisoi and Mishra [39] reported lower bound of the box size for accurate estimation.
In last three decades, fractal geometry (FG) has been the focus of attention by several researchers owing to it exhibiting excellent properties and robust application with respect to current research scenario. Fractal Dimension (FD) plays a vital role in order to analyse complex objects that are found in nature which was failed to be analysed by Euclidian geometry. FD is an imperative aspect of FG to provide indicative application in different areas of research including image processing, pattern recognition, computer graphics and many more. Analysis of an image is an important technique of image processing to describe image features like texture, roughness, smoothness etc., and is only possible through FG. Due to this reason many more technique were evolved to estimate the fractal dimension. The main aim of this article is to give a comprehensive review, which summarizes recent research progress on analysis of surface roughness and an overview of different concepts, and the way they work and their benefits and their limitations, and also we deliver how the different concepts taken into consideration to estimate FD depend upon different algorithms. This article also discusses several factors affecting FD estimation; types of similarity property, spatial resolution, sampling process, region of interest, spectral band and box-height criteria are discussed. Furthermore, we have tried to present the application area oriented versus core area of FG. There are several contradictory results found in many kinds of literature on the influence of different parameters while conducting FD analysis. Mainly it has been observed that the FD estimation will be affected by texture property, gray scale range, color property, color distance and the other parameters which are already mentioned. Hence this article will be beneficial for researchers in order to select precise FD estimation. However different algorithms lead to different results even with the use of the same kind of database images, so selection of appropriate technique is a major challenge for accurate estimation. Therefore an in-depth and proper understanding is required in order to choose the appropriate algorithm and also a robust algorithm for analysing roughness in better and precise way needs to be developed.
Feature selection for spontaneous speech analysis to aid in Alzheimer's disease diagnosis: A fractal dimension approach
2015, Computer Speech and Language
Citation Excerpt :
Thus, when appropriate data are available, linear systems can be implemented fairly rapidly, as they rely on well-known machine learning techniques to achieve their goals, avoiding complex adjustments to the system. The interest in fractals in speech date back to the mid-1980s (Pickover and Khorasani, 1986), and they have been used for a variety of applications, including consonant/vowel characterization (Martinez et al., 2003; Langi and Kinsner, 1995), speaker identification (Nelwamondo et al., 2006), and end-point detection (Li et al., 2007), even for whispered speech (Chen and Zhao, 2006). Recent research concerns the analysis of pathological voices through a fractal approach (Chouard et al., 2001; Ouayoun et al., 1999; Péan et al., 2000, 2002).
Alzheimer's disease (AD) is the most prevalent form of degenerative dementia; it has a high socio-economic impact in Western countries. The purpose of our project is to contribute to earlier diagnosis of AD and allow better estimates of its severity by using automatic analysis performed through new biomarkers extracted through non-invasive intelligent methods. The method selected is based on speech biomarkers derived from the analysis of spontaneous speech (SS). Thus the main goal of the present work is feature search in SS, aiming at pre-clinical evaluation whose results can be used to select appropriate tests for AD diagnosis. The feature set employed in our earlier work offered some hopeful conclusions but failed to capture the nonlinear dynamics of speech that are present in the speech waveforms. The extra information provided by the nonlinear features could be especially useful when training data is limited. In this work, the fractal dimension (FD) of the observed time series is combined with linear parameters in the feature vector in order to enhance the performance of the original system while controlling the computational cost.
Joint Sparsity and marginal classification for improving Sparse Imputation performance in speech recognition
2015, Computers and Electrical Engineering
Citation Excerpt :
For more explanation, it can be referred to the performed experiments in [12,13] showing that even with a small part of speech spectrum, still the remaining signal is understandable to the human listeners. On the other hand, in numerous references it has been pointed out that speech signal has considerable fractal properties in the time domain [14–16]. The fractal properties are closely related to self-similarity and in other words it means that different parts of speech, despite having time intervals from each other, could be potentially very similar and could have the same natures.
Sparse Imputation (SI) is a relatively new method that reconstructs missing spectral components of noisy speech signal with the help of the sparse-based representation approaches. In this method, the redundancy of signal in the frequency domain helps to rebuild noisy spectral components from the remained reliable ones. On the other hand different parts of speech signal, despite time intervals between them, can be inherently similar to each other. In this paper, a major modification over the SI method is proposed that in addition to data redundancy property of speech signal in small regions, takes the advantages of its self-similarity nature over long intervals. By identifying mostly similar frames, using a method based on the marginal classification, the Joint Sparsity method is applied and a method dubbed as the Joint Sparse Imputation is presented. The experiments conducted on AURORA 2 data set show that the proposed method significantly improves the recognition results in different noisy conditions, compared to the original SI method.
Feature selection for automatic analysis of emotional response based on nonlinear speech modeling suitable for diagnosis of Alzheimer's disease
2015, Neurocomputing
Citation Excerpt :
Thus, when appropriate data are available, linear systems can be implemented fairly rapidly, as they rely on well-known Machine Learning techniques to achieve their goals, avoiding complex adjustments to the system. The interest in fractals for speech signal processing date back to the mid-1980s [25]. Fractals have been used for a variety of applications, including consonant/vowel characterization [26,27], speaker identification [28], and end-point detection [29], even for whispered speech [30].
Alzheimer׳s disease (AD) is the most common type of dementia among the elderly. This work is part of a larger study that aims to identify novel technologies and biomarkers or features for the early detection of AD and its degree of severity. The diagnosis is made by analyzing several biomarkers and conducting a variety of tests (although only a post-mortem examination of the patients’ brain tissue is considered to provide definitive confirmation). Non-invasive intelligent diagnosis techniques would be a very valuable diagnostic aid. This paper concerns the Automatic Analysis of Emotional Response (AAER) in spontaneous speech based on classical and new emotional speech features: Emotional Temperature (ET) and fractal dimension (FD). This is a pre-clinical study aiming to validate tests and biomarkers for future diagnostic use. The method has the great advantage of being non-invasive, low cost, and without any side effects. The AAER shows very promising results for the definition of features useful in the early diagnosis of AD.
Fractal geometry for medical signal analysis: A review
2010, IRBM
Dans le cadre du diagnostic, l’interprétation des images médicales est une tâche complexe pour la détection des anomalies potentielles. Un des procédés les plus utilisés pour cette caractérisation est la texture. De nombreuses études ont été menées pour développer des algorithmes de quantification de la texture. L’intérêt de la géométrie fractale en analyse d’images médicales est justifié par l’auto-similarité des objets anatomiques sur une résolution finie. L’utilisation de cette géométrie repose principalement sur l’estimation d’attributs fractals. Diverses méthodes ont été proposées pour estimer la dimension fractale ou le spectre multifractal. Cette étude énumère l’ensemble de ces algorithmes, leurs principes, leurs avantages et inconvénients, ainsi que leur application dans le domaine de l’analyse des signaux médicaux.
The diagnostic interpretation of medical images is a complex task aiming to detect potential abnormalities. One of the most used features in this process is texture which is a key component in the human understanding of images. Many studies were conducted to develop algorithms for texture quantification. The relevance of fractal geometry in medical image analysis is justified by the proven self-similarity of anatomical objects when imaged with a finite resolution. Over the last years, fractal geometry was applied extensively in many medical signal analysis applications. The use of these geometries relies heavily on estimation of the fractal features. Various methods were proposed to estimate the fractal dimension or multifractal spectrum of a signal. This article presents an overview of these algorithms, the way they work, their benefits and limits, and their application in the field of medical signal analysis.

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Technical sectionFractal characterization of speech waveform graphs

Abstract

Physica

Computers & Graphics

J. Mol. Graphics

The Fractal Geometry of Nature

On the use of computer generated symmetrized dot-patterns for the visual characterization of speech waveforms and other sampled data

On the educational uses of computer-generated cartoon faces

J. Educational Technology Systems

Short-term phase characterization in dynamic signal analysis

IBM Tech. Discl. Bul.

Speech vectorgram

IBM Tech. Discl. Bul.

Use of symmetrized dot-patterns to produce polar graphs of speech waveforms

IBM Tech. Discl. Bul.

The problem of contiguity

How long is the coast of Britain

Science

Fractal fingers in viscous fluids

Science

Fractal symmetry

Mosaic

Computer recreations

Scien. Amer.

A place in the sun for fractals

Science News

Generation and display of geometric fractals in 3-D

Computer Graphics

Fractals

Byte

Die unendliche reise

Geo

Technical section
Fractal characterization of speech waveform graphs